000			02055nam a22002655i 4500
001			u4935
003			SIRSI
005			20250825175020.0
008			181017s2018 gw r 000|0 eng c
020			_a3319984071
082	0		_a515.353 _223
100	1		_aEfendiev, Messoud, _eauthor.
245	1	0	_aSymmetrization and Stabilization of Solutions of Nonlinear Elliptic Equations / _cby Messoud Efendiev.
250			_a1st edition 2018.
264		1	_aCham : _bSpringer International Publishing : _bImprint: Springer, _c2018.
300			_axvii, 258 pages.
490	1		_aFields Institute Monographs ; _v36
504			_aBibliography: pages 253-258.
505	0		_tPreface -- _t1. Preliminaries -- _t2. Trajectory dynamical systems and their attractors -- _t3. Symmetry and attractors: the case N ≤ 3 -- _t4. Symmetry and attractors: the case N ≤ 4 -- _t5. Symmetry and attractors -- _t6. Symmetry and attractors: arbitrary dimension -- _t7. The case of p-Laplacian operator -- _tBibliography.
520			_aThis book deals with a systematic study of a dynamical system approach to investigate the symmetrization and stabilization properties of nonnegative solutions of nonlinear elliptic problems in asymptotically symmetric unbounded domains. The usage of infinite dimensional dynamical systems methods for elliptic problems in unbounded domains as well as finite dimensional reduction of their dynamics requires new ideas and tools. To this end, both a trajectory dynamical systems approach and new Liouville type results for the solutions of some class of elliptic equations are used. The work also uses symmetry and monotonicity results for nonnegative solutions in order to characterize an asymptotic profile of solutions and compares a pure elliptic partial differential equations approach and a dynamical systems approach. The new results obtained will be particularly useful for mathematical biologists.
650		0	_aPartial differential equations.
650		0	_aDynamics.
650		0	_aErgodic theory.
830		0	_aFields Institute Monographs ; _v36
999			_c3498 _d3498